14,161 research outputs found
Direct Inversion of Digital 3D Fraunhofer Holography Maps
The Differential Fourier Holography (DFH) gives an exact mathematical
solution of the inverse problem of diffraction in the Fraunhofer regime. After
the first publication [1] the Differential Fourier Holography was successfully
applied in many experiments to obtain amplitude and phase information about
two-dimensional (2D) images. In this article we demonstrate numerically the
possibility to apply the DFH also for investigation of unknown 3D Objects. The
first simulation is made for a double-spiral structure plus a line as a
reference object
Observation of topologically protected helical edge modes in Kagome elastic plates
The investigation of topologically protected waves in classical media has
opened unique opportunities to achieve exotic properties like one-way phonon
transport, protection from backscattering and immunity to imperfections.
Contrary to acoustic and electromagnetic domains, their observation in elastic
solids has so far been elusive due to the presence of both shear and
longitudinal modes and their modal conversion at interfaces and free surfaces.
Here we report the experimental observation of topologically protected
helical edge waves in elastic media. The considered structure consists of an
elastic plate patterned according to a Kagome architecture with an accidental
degeneracy of two Dirac cones induced by drilling through holes. The careful
breaking of symmetries couples the corresponding elastic modes which
effectively emulates spin orbital coupling in the quantum spin Hall effect.
The results shed light on the topological properties of the proposed plate
waveguide and opens avenues for the practical realization of compact, passive
and cost-effective elastic topological waveguides
A Bayesian Approach to Manifold Topology Reconstruction
In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated
An accurate boundary value problem solver applied to scattering from cylinders with corners
In this paper we consider the classic problems of scattering of waves from
perfectly conducting cylinders with piecewise smooth boundaries. The scattering
problems are formulated as integral equations and solved using a Nystr\"om
scheme where the corners of the cylinders are efficiently handled by a method
referred to as Recursively Compressed Inverse Preconditioning (RCIP). This
method has been very successful in treating static problems in non-smooth
domains and the present paper shows that it works equally well for the
Helmholtz equation. In the numerical examples we specialize to scattering of E-
and H-waves from a cylinder with one corner. Even at a size kd=1000, where k is
the wavenumber and d the diameter, the scheme produces at least 13 digits of
accuracy in the electric and magnetic fields everywhere outside the cylinder.Comment: 19 pages, 3 figure
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